NASA TECHNICAL TRANSLATION
NASA TT (12,106
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AN EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER
IN THE NOZZLE OF HIGHALUMINI2ED SOLID ROCKET
(EFFECTS OF ALUMINUM ADDED TO PROPELLANT)
Tomlfumi Godai, YoshJnori Yuzawa
Katuya Ito and Hisao Nishimura
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Technical Report of National Aerospace Laboratory,
TRU7, Tokyo (Japan), I968, 10 pages
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON, D.C. 205^6 FEBRUARY 1969
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NASA TT F12,106
AN EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER
IN THE NOZZLE OF HIGHALUMINIZED SOLID ROCKET
(EFFECTS OF ALUMINUM ADDED TO PROPELLANT)
Tomlfumi Godai^ Yoshinori Yuzawa
Katuya Ito and Hisao Nishimura
ABSTRACT. The heat transfer in the nozzle of a highalumlnized
solid rocket has been experimentally investigated.
It Is noted that the addition of metallic fuel to the
propellant has a pronounced effect on the heat transfer co
efficient but that the radiant heat flux Is not dominant In
such a nozzle.
It Js also notec that Bartz's treatment may be applied
to the heat transfer problem in a mixed gasparticle flow,
assuming that the gasparticle flow behaves like the gas flow
with equivalent specific heat ratio »c.
The equivalent specific heat ratio is obtained, where
the velocitylag of the particle behind the gas flow is
negl igibly smal 1 . '
An experimental study was made of the heat transfer
In a solid rocket mortar nozzle using a polybutadiene
system composite propellant containing aluminum. It was
found that the rate of heat transfer increases markedly as
the alCiminum content In the propellant is increased, and
that the effect of heat radiation of alumina particles was
small. Moreover, in computing the heat transfer, the com
bustion gas flow containing alumina particles was treated as
a single gas phase flow having mixed phases and equivalent
specific heats, and it was found that the results of com
putattpn obtained by applying the semitheoretical equation
pertaining to turbulent flow heat transfer within a tube
matches well with the experimental values.
1. INTRODUCTION:.
Charactei^istics such as the specific thrust of solid rocket propellants
have improved greatly in recent years. There are reasons for this progress;
we can consider advances in research on oxidants, fuel binders, and
catalysts which are propellant components, together with the effects obtained
by the addition of metal fuels such as aluminum powder to them. However,
while the addition of metal fuels serves to improve the specific thrust, they
make the heat conditions in the nozzle section more severe. In propellants
containing large quantities of aluminum, there is much greater damage done
to the nozzle throat section in comparison with propellants not containing
aluminum, and ablation is particularly severe with plastic nozzles. Because
of this it is considered to be the elevation of temperature of the combustio n
•Numbers in the margin indicate pagination in the foreign text. ~
/V
gas duo to the burning of the aluminum, and the effects of the coagulate!
particles of alumina. It \s a well known fact that if one assumes that
the combustion gas is a perfect gas, and that the reaction ^n the process
of expansion in the nozzle is frozen, the results of computation obtained
by application of Bartz's semi theoretical equation [1,2] for turbulent flow
heat transfer within a tube agree well with experimental values, in the case
of a heat transfer within a rocket motor nozzle using propellants that do
not contain metal additives. However, the weight ratio of alumina in the
combustion products in a propel lant containing 20% aluminum, reaches
as much as 50%, and the method of treating the effects of this ratio poses
a problem*
We have conducted an experimental study of heat transfer in a solid
rocket motor nozzle, using a polybutadiene system composite propellant,
containing no aluminum, 10% aluminum and 20% aluminum, and have attempted
to do a theoretical analysis of the results.
/2
2. SWBOLS;
A:
C :
P
D:
E:
F:
I:
I ;
sp
M:
P:
P :
r
Q:
R:
W:
a:
c:
c*:
d
f
g
h
k
I
m
n
q
r
t
u
Y
Area .
Specific heat at constant pressure
Nozzle diameter
Nozzle throat area ratio
Thrust
Volume ratio
Specific Thrust
Mach
Combustion pressure
Prandtl number
Heat capacity
Gas constant
Weight
Average cross section area of particle
Specific heat
Characteristic exhaust gas rate
Particle diameter
Configuration coefficient
Acceleration of gravity
Heat transfer coefficient
Heat conductivity
Distance
Average inolecular weight of gas
Number of particles per unit volume
Heat transfer volume
Radius of curvature of nozzle throat
Time
Velocity
Specific Weight
mm
m^
mm
1.
•
t •
Monocliromatic radiation rate
0:
Temperature
y:
Viscosity coefficient
p:
Density
o:
Boltzmann's constant
<:
Specific heat ratio
SUBSCRIPTS:
c:
Convection flows
0'
Gas
c:
Stagnation point
P
Particle
pp:
Propel 1 ant
r:
Radiation
t:
Throat
w:
Wall
z:
Point
3. METHOD OF EXPERIMENT
In this investigation, it was decided to determine the rate of heat
transfer by measuring the temperature changes of plugs placed perpendicular
to the wall surface in several places within the nozzle. Many thermo
couples are required in this method, but it is well known that in cases such 
as a solid rocket, the combustion time is relatively short, and it is
possible to obtain highly acurate results in the case where it is difficult
to obtain a thermally stable state [3].
If we consider here that the surrounding surface of the plug which is
u?ed for measuring heat transfer is completely heatinsulated except on the
heat transfer surface and in the c .tremity, it is possible to view the plug,
in terms of heat, as a single dimension model. The increase in heat capacity
per unit of time can be expressed as
*^wb°^AT^\ ' "'
since it is equal to the heat flux q which enters through the heated surface, I
and if we assume that the heat loss from the outer end is ^j^ji ' 0. then the 
rate of heat flow into a plug with a length, I, and a constant cross section 
area, A, in the time interval between t^ and t2 is: 
I
4l»UliJi. l I ' l J J ' . I ..Jl' W l ' I f ll H llli p
Consequently, the heat transfer rate h is computed by
(3)
The plugs were made of. pure copper which have a high temperature
conductivity, in order to avoid losses on the heating surfaces, and in
order to minimize the heat exchange with the surrounding parts, the plug
was placed in a nozzle made of the same material.
/3
QZEZD"*^
F!g, ^ 1: Model of Copper PI
ug
As shown in Figure 2, two models (I, II) with differing plug positions for
temperature measurement were used for the nozzles that were tested, in
model (I) the five points A, B, C, D, E, and in model (11) the five points
A, B', C, D*. E' are the positions of plug attachment. In each case c
corresponds to the throat section.
Copper plugs
MM
Mmmm
mmmmmm
Position
Noxzlc type
Plug position and throat area ratio
A
B
4$
B*
C
1.0
h'
D
E'
£
I
10
4.0
11. «
10
LO
1.3
1«*
Fig. 2: Cross Section and Plug
Poslt'on in Nozzle Used fcr
Measuring Heat Transfer
As indicated in Figure 3, two holes one mm deep and 0,4 mm in diameter
were made at a distance of 1 mm from each other on the periphery of one
plug. After inserting an alumel wire 0.3 mm in diameter and a chromel wire
of the same diameter into these holes, thermocouples were placed in four
spots at distances of 8, 13, 20, and 28 mm from the end of the heated area.
A total of 20 thermocouples ^^^ used. In order to reduce the area of
contact of the plug and the nozzle wall, they were made to fit closely and
the section of the plug protruding into the nozzle inner wall was shaved off,
so that it was uniform with the nozzle inner wall. This means that the
distance from the heated surface to the thermocouple differed from the 8,
13, 20, and 28 mm described above, so after tests, these were measured
acurately by removing the plugs. Furthermore, in order to reduce the heat
fluctuation due to conduction currents in the space around the plug, the
gap between it and the nozzle itself was reduced.
L,
■R
f 28
p— 20 — 
J,
^^^
b^^^^
— so
t
Fig, 3: Plug Configuration and Position of
Thermocouple Insertlon^
The propellant used in the tests was a polybutadiene composite with
ammonium perchlorate as the oxidant. The configuration is shown in Figure 4.
The diameter is 93 mm, length 327 mm and weight 2.6 kg. Since the heat
transfer rate differs depending on the combustion gas pressure, flow velocity
mm
\ {
Register
V
Propcliant
Fig. k: Configuration of Propellant
I
'"'W^ n
Fig. 5.
and flow rate, the internal con
figuration of the propellant was
selfjcted so that these values
would remain as constant as
possible during measurement of
heat transfer, i.e. so that the
thrust would remain as constant
as possible. For the propellant
three vaf'ielies were used, one
not containing aluminum powder,
one with 10% and one with 20%
aluminum. The average particle
diameter of the aluminum powder
used was ]9 y. The propellant
composition is shown in Table 1.
The rocket motor burning
test was conducted on a one ton
lateral test stand in the solid
rocket laboratory. Figure 5
shows the rocket motor on the
test stand. Resistance wire
strain gauge type pickup5 were
used for measuring the thrusts
and combustion pressure, and
the apparatus was designed so
that these measurements, along
with measurements of temperature
could be recorded on a direct
vision electromagnetic oscil
/4
lograph. The thermocouples used for measuring temperature throughout the
measuring system, were calibrated at 20**C, 60*C and 80*C, with the melting
points of tin, lead, and zinc prior to the tests.
Table 1.: Composition of Propellent
Propellanr
Composition n^^gj^,, ^uta
Aluminum
Powder
PropenantwithO%*Al
Propellant with iO%* A]
Propellant with 207(/* Al
^Percentage increase to gross weight
The burning tests for each propellant were conducted under conditions
where IC. (ratio of combustion area to nozzle throat area) were constant. As
explained below, for propel lants with a 0% and 10% aluminum content data were
obtained for four burning tests, but in the case of propellant containing
20% aluminum, in the two burning tests that were conducted, the nozzle throat
m^
mmm
was burned up 0.6 seconds after ignition both times. For this reason, for
the propellant with 20% aluminum, the pure copper nozzle was replaced with a
graphite nozzle and separate burning tests were conducted.
4. Test Results
The results of burning tests of each propellant are shown in Table 2 below.
Table 2.: Burning Tests Results
Type of Propellant ^ Propellant with Q^o Al ' Propellant with 10% Al Propr \ \ ant with 20% Al
^""'"^.■I?^^ : 1 T213 4il2 3 A \ I \ I 3*'
^_Test
Observation"^'^— ~^ !
Minimum Pressure V'min' 39.3 kg/cm»' 38.5 J 41.5 ! 41.2 j 48 S
Maximum Pressure'/' mux
Propellant Weight
Specific Thrust *
52,3 kgW 54.4 ; 55.1 I 59,5 I 69.5
2.486 kg ^2.478 2.477 2.468 ,2.590
213 sec
 211
211
49.5 53.3
70.3 71.1
2.585 2576
46.9
2'6Z
221
226
52.5
70.3
!2.545 2.676 2.683
227
53.7
48.5
60.2
2.677
226
* Results from graphite nozzle
One example of the tbrusttime curve is shown in Figure 6. In each case
the thrust was SOU kg, the combustion pressure 50 kg/cm^, and the burning time
was two seconds. It was decided to read the temperature data for calculating
the heat transfer rate off the recording paper in the interval during which
the burning state can be regarded as almost steady, avoiding the unsteady
burning time* ipnediately after ignition, since the heat transfer rate is
largely determined by the physical values of the gas. In Figure 7, the dis
tance from the thermocouple on the copper plug tj the nozzle wall is parted
on the Xaxis and the temperature at these points is parted on the yaxis
(logarithmic axis). The wall temperature 9 is determined by extrapolation
since it is expressed by a primary equation in a theoretically semiloga
rithmic coordinate system, if one assumes that there is no loss from the
periphery of the nozzle, and the heat transfer rate is also steady. Moreover,
the temperature distribution between each measuring point within the plug
is expressed as a primary equation, and the heat transfer volume i{ .At. + t )
was calculated from equation (2) .
/5
u
400
^5r:cr:~'='« — *^^^^ Propellant with 2
*too
100
<
wlthO^oAV \A \
Propellant with 10% Al ^''^^^sJ^n^
iV ■' l'6 L» zo ^
xy thrust
Fig. 6: Thrust*tlme Curves
mmmm
10 20 30 mm
'*<* Distance from nozzle wall
Fig. 7: Temperature Distribution
on Plug at Point E* in the Case
of a Propellant with 10^ Al
5, ANALYSIS
5.1 Alumina particles in combustion gas.
It is considered that the diameter and size of alurriina particles pro
duced by the burning of aluminum gradually increase as the alun.ina themselves
collide and fuse together repeatedly within the nozzle f4, 5, 6], However*
there are reports concerning the particle diameter of alumina which is
ejected from the nozzle, stating that the diameter varies according to
combustion pressure [7], and reports that the diameter is 23 y regardless
of combustion pressure [8] . However, it is considered a fact that the
diameter of the alumina particles varies according to the aluminum content
in the propellant [9, 10].
Even if the diameter of the alumina particles in the nozzle increai s
due to collision and bonding, in the case of propellant containing 20%
aluminum, it is reported that the diameter of particles ejected ;:hrougli the
nozzle is below 4.5 p at a combustion pressure of 70 kg/cm' [10], and even
if one calculates and compares the gas velocity and the alumina particle
<»i tfr i ftMfa .iii> >Wiiii ftf [  "irif  ^f„.,^ ^'=^^Wff\^,ntv ,^ w \im
sxi^'AJM aaaflaiiiSisaaa<i5affw,«iiMttMffti'niw^
velocity inside the nozzle, there is no great difference when the particle
diameter is less than several u, and the temperature difference betwe^rn the
gas and the alumina particljs is si.iall.
Here we shall consider the flow in the nozzle on the basis of the
following conditions.
(1) There is no loss of mass or energy from the system.
(2) There is no variation in mass between phases.
(3) The alumina particles do not cause a reaction, and the volume
occupied by them may be disregarded.
(4) The gas is a constant component and is considered to be a perfect
gas.
(5) The specific heat of the gas and alumina particles is assumed to
be constant.
The energy equation for the gas and alumina particles is
+ %[cpp(ffp'^po)+^tz/^^0
n) /6
As we have already noted, since the alumina particles that are produced are
very small, if we a.ssume that the temperature difference and the velocity
difference between the gas and the particles may be disregarded, we can find the
equivalent specific heat ratio of the mixed flow of particle and gas k. If,
in equation (4) we assume u
u = u, 9
g ' P
0=0
g
.(5)
Here, < is the specific heat ratio only for the gas phase.
That is, we can regard the two phase flow of gas and particle as a gas
phase in which the specific heat ratio is F.
>f>'itttaay.»j;i:'AMMi?Wiiiti«tf ^ njkimi ^t<agr tDjaV i r. tti r^ v :l^v «
iWi<»r>wit^iiirt:^iirn'MtWi iM ''rnr \^j^itimkik uaio iim r'7Tfi fA«i^,»^^^iUMiii^i'ii!»iiti>'i''''^'^^^ i^^tiS^i^iiiSiAitifiSimMi^i iWM'^^IB
If we "consider the nozzle gas to be an ideal gas, the gas velocity in the
nozzle u is
g
A/x V
l^~iA/x«
l^~^^f^
*^
(6)
If the specific heat ratio k is determined, it is possible to compute the
Mach nuKiber M at point x with respect to the aperture ratio E*
5.2 Physica? values of combustion products
Since in this test we are not measuring the combustion gas temperature,
specific heat ratio, or the average modular weight, these values were deter
mined from the results of tests on the composition of the propellant, combus
tion jpressure and specific thrusts, and from the literature [9, 10, li].
The specific heat ratio is calculated from equation (S) but the percen
tajge of alumina contained in the products of combustion in equation (5) W /iV^
was determined assuming that all of th^ aluminum underwent reaction in the
propellant, forming alumina." The results are shown below in Table 3,
I ■
Table 3: Alumina Weight Ratio in 5*3 Convection flow heat
Products of Combustion transfer rate
Considerable tests of heat
transfer in nozzles of rocket
motors, which do not contain
powdered metal such as aluminum,
have been made up to the pre
sent time, and semitheoretical
equations have been obtained.
Of these, Bartz's equations
agreed well with the test values, and are used in calculating heat transfer
in nozzles. Tho convection flow heat transfer volume q

wp^k ^
Propellent with O^^AI
Propellant with lO^o Al
Propellant with 20% Al
0.17
0.48
i<^hc(0g^0^)
(7)
Here^. using Bartz's semitheoretical equation, the convection heat transfer
rate h^ is
c
'^^
In this equation the heat transfer volume is validly determined by the per
centage of flow of mass per unit area.
10
rfrmriHifaittTyireiiMiww
m
I
The convection flow heat transfer was computed on the basis of (7) .
5*^ Radiant Heat Transfer
The radiant heat transfer volume q from the alumina particle cloud to the
nozzle wall is expressed by the following equation.
(10)
As for the radiant heat transfer between particles, we consider the
alumina particle to be spherical, and assuming that the temperature of a part
icle is almost equivalent to that of the neighboring particle, and that the
heat transfer within the ambient gas is negatibly small, if we assume that heat
transfer occurs only from the alumina particles to the nozzle wall, f = 1, and
equation (10) becomes
4r^'wp'<r{e,^^0„*) (11)
or '
'*,=len«t (12) I
(See 12), j
Expressing the gas velocity at a point where the nozzle inner diameter 
is D as u , and the specific weight of the alumina particles as y , since j
g P ^
the gas volume passing through the nozzle in a unit of time is j • D^ * u , the )
relative volume of the generated gas and the alumina particles I is I
1
T (13)
W is the alumina particle volume of particles passing through the nozzle
in a unit of time.
(14)
Whereupon,
11
,■ vi"
FPV'TC'"
6 '
Substituting equations (13) and (14) in equation (15) ,
na/=. ? ( ^P \ F
(15)
(16)
Therefore, the effective radiation rate e of the alumina particle cloud can
be determined, given small use of u , y , and d . Moreover, the radiation rate
^ g p p
of the nozzle wall z can be considered to be almost constant when the nozzle
w
wall temperature is below lOOO^C. From the above, the radiant heat transfer
rate q can be computed by equation (11).
A
eo a
•Ai • Fropcllant
•Aiio Propellant
g ^af
~« & 5l7 ai a5 t5 u ^T"
*•'*' Time (sec)
Fig. 8: Variation in Heat
Transfer Kate at Point A
•AiM Propellant
•ju« Propellant
6. Examination of Results ^9
Figures 8 and 9 show variation in the
heat transfer rate at points A and £•
during combustion. This variation is
almost stable with respect to the passage
of time. This is because the flow rate
of products of combustion passing through
the nozzle during that interval is almost
constant and as shown in Figure 10,. if
we determine the heat transfer rates at
0.50.6 seconds and 1.01.1 seconds and
compare them, we see that they are almost
constant regardless of the presence or
absence of aluminum in the propellant.
Figure 11 indicates the results of
tests on the effect of the percentage
of aluminum contained in the propellant
on the heat transfer rate. Clearly, as
the amount of aluminum is increased, the
heat transfer rate shows larger values,
in particular a value two times greater
is indicated in the throat section. As
for the heat transfer rate in the case of
propellant containing no aluminum, 0.50.6
seconds after ignition, as shown in Figure 12, the experimental values and the
theoretical values for the convection flow heat transfer rate agree well,
except in the fanshapsd section of the nozzle. There is a good match between
experimental and theoretical values 1.01.1 seconds after ignition, as sho\m
in Figure 15, except in the throat section. Figures 13 and 14 show the distri
bution of the heat transfer rate in the case of propellant containing 10% and
■* ii A — jfj — 5&I — 19 — i!5 — rt — tr
Time (sec)
Fig.. 9: Variation in Heat
Transfer at Point E*
12
NM
rffimrinpftimw
feiWiWifniwirrrTijiinrirwMiMiinn^ii
?
iiii,»Aito«Propcllant
j>ec»Ai Ki Propellant
««j«Aiic;5 Propellant
eci^Ai 0:; Propellant
T
20% aluminum respectively, at 0.50.6
seconds. It can be seen here, that there
is a rather good match between computed
values of conduction flow heat transfer
and test values. The magnitude of the
radiant heat transfer from the aluminum
particles is smaller than the conduction
flow heat transfer, but the computed va 
ues in which corrections are made for
radiation, indicate a closer approximation
with respect to the test values. The
radiant heat transfer rate is particularly
great in the vicinity of the nozzle inlet.
Figures 15 and 16 indicate the distribution
of the heat transfer rate 1.01.1 seconds
after ignition. Generally a slight dif
ference can be observed between theoretical and test values in the nozzle throat
section, but this is considered to be due to scattering in the tests.
RR' C 0* D E' E
(Throat)
Position inside nozzle
rjg, 10: Comparison of Heat
Transfer Rate in Nozzle at
Time 0.50.6 Seconds and
1 .01 . 1 Seconds
4)
Test results
Ai2o%Piopellant
"Ano^ Propellant
l^AiOfi Propellant
1. unu 1
y Position inside nozzle
.2
cd
ti
o Test values
"Values ftom Bartz*s
equations 0.50.6 seconds
BB'
C D'
E'
Position inside nozzle
Fig. 11: Effect of Aluminum
Content in Propellant on the
Heat Transfer Rate in the Nozzle
Section (Test Results 0.50.6
Seconds after Ignition)
Fig. 12: Heat Transfer Rate
Inside Nozzle in the Case
of Propellant w*th 0% Al
1 i
k»l/«tfl1C
.«tt 4
X
• Test values
— Values from Bartz's
A equation
—Values obtained when adding
" ^' the radiation equation to
Bartz*s 0.60.6 seconds
heil/KUt;
1 — a nu I
, Position inside nozzle
Fig, 13: Heat Transfer Rate Inside
Nozzle in Case of Propellant with
]0% Al
■® Test values
— Values from Bartz*s
equation
—Values obtained when
adding the radiation equ
ation to Bartz*s equation
0,60.6 seconds
Position inside nozzle
Ftg. \k: Heat Transfer Rate
Inside Nozzle In the Case
of Propellant with 20% Al
13
I .
aiW Mir mm r
glfflllWiTiiffiiWWirTHIJfii
r>MiiaytfittiiiiiBjifrfftfHir!inBimwipni
jtawiflitffTiftfiKnrirrfr
^xtUmliC
Test values
Values from Bariz's
equation 1.0Ll seconds •
TTSTT
Position inside nozzle
Fig. 15: Heat Transfer Rate Inside the
Nozzle In the Case of Propellant with
0* Al
t<«l/»UX
• Test values
— Values from Bartz's
equation
— Values obtained by
adding radiation equa
tion to Bartz's equation
L 01.1 Seconds
Fig, 16:
Nozzle
10* Al
Position inside nozzle
Heat Transfer Rate Inside the
in the Case of Propellant with
7. Conclusion
. The following facts were deter
mined from this experimental study.
(1) There is a marked increase
in the heat transfer rate inside
the nozzle as the amount of 'alum
inum contained in the propellant
is increased.
(2) Even when the propellant
contains 20% aluminum, the influ
ence of radiation from aluminum
particles on the nozzle heat trans
fer is small, the major influence
being from conduction flow heat
transfer.
(3) The computed values for
the conduction flow heat transfer
almost match the test values when
computed using Bartz*s semitheo
retical equation, even for propel
lant containing large amounts of
aluminum, if we assume the mixed
flow of gas and alumina particles
go through the nozzle as a gas
phase with an equivalent specific
heat ralio F.
Finally, we would like to express
our gratitude to the personnel in
the rocket division beginning with Division Chief Kuroda, and to Technical
Officer Sekine of the Engine Section for their guidance and cooperation through
out this study.
REFERENCES
1. Bartz, D. R», "A Simple Equation for Rapid Estimation of Rocket Nozzle
Convective Heat Transfer Coefficients'/ Jet Propulsion^ p. 49, Jan. 1957.
2, Bpttz, D, R., "An Approximate Solution of Compressible Turbulent Boundary
layer Development and Convective Heat Transfer in ConvergentDivergent
Nozzles, "Transactions of the ASME, pp, 12351245; November, 1955,
3. Liebert, C. H,, J. E. Hatch and R. W. Grant, "Application of Various
Techniques for Determining Local Heat Transfer Coefficient? in a Rocket
Engine from Transient Experimental Data", NASA TN 0^2??, 1960.
4, Sehgal, R., "An Experimental Investigation of a Gas Particle System,"
Jet Propulsion Lab TR''32238, 1962.
14
w»«
mmm
Msm
5. Brown, fi. and F. P. McCarty, "Particle Size of Condensed Oxide from Com
bustion of Metallized Solid Propellant," P/oceedings of the 8th Inter
national Combustion Symposium, pp* 814823, 1962,
6. Crowe, C. T. and P. G. Willoughby, "A Study of Particle Growth in a Rocket
Nozzle", AIAA Paper 66639, 1966.
7. Cheung, H. and N, S. Cohen, "On the Performance of Solid Propellants Con
taining Metal Additives," AIAA preprint, 64116, 1964.
S. Crowe, C. T. and P. G. Willcughby, "A Mechanism for Particle Growth in a
Rocket Nozzle," j1IA4 Journal, pp. 16771678, Sept. 1966.
9. Sutton, G, P,, Rocket Prop74lsion Elements, John Wily § Sons, 3rd pp. 174
177, 1963.
10. Ciepluch, C. C, "Spontaneous Reignition of Previously Extinguished
Solid Propellants," NASA TN D216?, 1963.
11. Zeleznih, F. J. and S. Gordon, "A General IBM 704 or 7090 Computer
Program for Computati'^n of Chemical Equilibriu ' Composition. Rocket
Performance and ChapmannJouget", MSA TN D14S4, 1962.
12. Hottel, H. C, "Radia>xtHeau Transmission^* in Heat Transmission,McMms ed.
1954.
Translated for the National Aeronautics and Space Administration under Contract
No. NASw1695 by Techtran Corporation, P.O. Box 729, Glen Burnic, Maryland
21061
IS
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